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Inelastic diffraction of fast atoms on crystal surfaces a Lamb-Dicke regime in shallow atomic collisions

Maxime Debiossac, Peng Pan, P. Roncin

Published Jul 1, 2019• 0 citations
OpenAlex

Abstract

Synopsis Grazing incidence fast atom diffraction (GIFAD) uses keV atoms to investigate properties of crystal surfaces. It exists in two flavors; The elastic diffraction is identified by bright spots sitting on the Laue circle of energy conservation. We will focus on inelastic diffraction with a model where the surface atoms are quantum harmonic oscillators and where the successive collisions of the projectile take place in the Lamb-Dicke regime. The model explains observed lines shapes and predicts a drastic dependence of the energy loss ∆E ∝ θ 7 .

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Synopsis Grazing incidence fast atom diffraction (GIFAD) uses keV atoms to investigate properties of crystal surfaces. It exists in two flavors; The elastic diffraction is identified by bright spots sitting on the Laue circle of energy conservation. We will focus on inelastic diffraction with a model where the surface atoms are quantum harmonic oscillators and where the successive collisions of the projectile take place in the Lamb-Dicke regime. The model explains observed lines shapes and predicts a drastic dependence of the energy loss ∆E ∝ θ 7 .
Coherence properties of projectiles, found relevant in ion-atom collisions, are investigated by analyzing the influence of the degree of coherence of the atomic beam on interference patterns produced by grazing-incidence fast-atom diffraction (GIFAD or FAD). The transverse coherence length of the projectiles, which depends on the incidence conditions and the collimating setup, determines the overall characteristics of GIFAD distributions. We show that for atoms scattered from a LiF(001) surface after a given collimation, we can modify the interference signatures of the angular spectra by varying the total impact energy, while keeping the normal energy as a constant. Also, the role played by the geometry of the collimating aperture is analyzed, comparing results for square and circular openings. Furthermore, we study the spot-beam effect, which is due to different focus points of the impinging particles. We show that when a region narrower than a single crystallographic channel is coherently illuminated by the atomic beam, the spot-beam contribution strongly affects the visibility of the interference structures, contributing to the gradual quantum-classical transition of the projectile distributions.
Diffraction of fast helium atoms at alkali-halide surfaces under grazing angles of incidence shows intriguing diffraction patterns. The persistence of quantum coherence is remarkably strong, even though high surface temperatures and high (keV) kinetic energies of the incident atoms would strongly suggest the dominance of dissipative and decohering processes. The main source of decoherence is the excitation or absorption of surface vibrations upon impact. The momentum transfer between the surface and the incident helium atom depends on the amplitude of the thermal vibrations of the surface atoms and the energy of the incident particle. We present an ab initio simulation of the quantum diffraction of fast helium beams at a LiF (100) surface in the (110) direction, and compare with recent experimental diffraction data.
The coherence for diffraction effects during grazing scattering of fast hydrogen and helium atoms from a LiF(001) surface with energies up to some keV is investigated via the coincident detection of two-dimensional angular distributions for scattered projectiles with their energy loss. For keV H atoms, we identify electronic excitations of the target surface as the dominant mechanism for decoherence, whereas for He atoms this contribution is small. The suppression of electronic excitations owing to the band gap of insulators plays an essential role for preserving quantum coherence and thus for the application of fast atom diffraction as a surface analytical tool.
The semiclassical perturbation method developed by Henkel et al. [J. Phys. II 4, 1955 (1994)] to model cold-atom diffraction by optical standing waves, is applied to the diffraction of fast atoms on crystal surfaces at grazing incidence (GIFAD or FAD). We first show that the interaction time and interaction length embedded in the obliquity factor is well suited to explain the transition from three-dimensional to two-dimensional (2D) diffraction. The situation of a slightly misaligned primary beam, corresponding to oblique incidence in the effective 2D system, is addressed pointing out discrepancies such as the absence of net deflection of the atomic beam. Guided by time-reversal considerations, we propose an arbitrarily symmetrized form significantly improving the agreement with experimental data recorded in oblique incidence.
Scattering of fast neutral atoms with keV kinetic energies at alkali-halide surfaces under grazing angles displays intriguing diffraction patterns (Schuller, Wethekam and Winter 2007, Roisseau et al. 2007). In spite of the impulsive interaction with a surface at elevated temperature, which results in phonon excitation, quantum coherence evidently persists. To quantitatively study this remarkable survival of coherence, we present an ab initio simulation of the quantum diffraction of fast helium beams at a LiF (100) surface in the 〈110〉 direction and compare with recent experimental diffraction data. Decoherence is analyzed employing a quantum trajectory Monte Carlo method (Minami, Reinhold and Burgdorfer 2003), calculating the ensemble average over solutions of a stochastic linear Schrodinger equation. The evolution of the atomic wavepacket is governed by a sequence of stochastic collisions and continuous propagation in the He-LiF surface potential. We find near-perfect agreement between the resulting diffraction patterns and experimental results (Schuller, Wethekam and Winter 2007) without using any adjustable parameters. The question, whether the LiF surface features “buckling”, (i.e. vertical surface reconstruction where the F atoms are displaced relative to the Li atoms) has been addressed in the past (de Wette, Kress and Schroder 1985). However, experimental uncertainties were of the same order as the displacement amplitude itself. In atom-surface diffraction at a grazing angle, surface reconstruction drastically changes the diffraction patterns. By comparison of numerical and experimental results, the buckling amplitude can be determined with unprecedented accuracy.
Scattering of fast neutral atoms with keV kinetic energies at alkali-halide surfaces under grazing angles displays intriguing diffraction patterns. The surprisingly strong persistence of quantum coherence despite the impulsive interaction with an environment at solid state density and elevated temperatures raises fundamental questions such as to the suppression of decoherence and of the quantum-to-classical crossover. We present an ab initio simulation of the quantum diffraction of fast helium beams at a LiF (100) surface in the 110 direction and compare with recent experimental diffraction data. From the quantitative reconstruction of diffraction images the vertical LiF-surface reconstruction, or buckling, can be determined.